Question

Consider two lines $L_{1}: \frac{x-7}{3}=\frac{y-7}{2}=\frac{z-3}{1}$ and $L_{2}:$ $\frac{x-1}{2}=\frac{y+1}{4}=\frac{z+1}{3}$. If a line $L$ whose direction ratios are $\langle 2,2,1\rangle$ intersect the lines $L_{1}$ and $L_{2}$ at $A$ and $B$ then the distance $A B$ is

Answer 1

$A \equiv 3 \lambda+7,2 \lambda+7, \lambda+3$
$B=2 \mu+1,4 \mu-1,3 \mu-1$
$\therefore \frac{3 \lambda-2 \mu+6}{2}=\frac{2 \lambda-4 \mu+8}{2}$
$=\frac{\lambda-3 \mu+4}{1}$

$\therefore \lambda=2$ and $\mu=0$
$\Rightarrow A \equiv(13,11,5), B=(1,-1,-1)$
$\therefore A B=18$